I wrote a review for the first season with a whole lot of complaints, and although I certainly liked the second season better than the first, I still had some problems with it.
Ciel and Sebastian remain two-dimensional characters. They haven't gained any new character development as the season changed. The sad thing is that it almost appears that Alois is the one with the most character development, and he's not even a likable character through anything but pity over his constant rejections from Claude.
The story was definitely improved from the first season, although I am aware that the second season was an original plot that was not part of the manga. It had more depth (although sadly, as I mentioned, the characters failed to match the depth of the story itself) and was vastly entertaining.
However, when problems with the first season were taken away, this season gained new problems.
Season two was an explosion of fanservice, from Alois's implied sexual obsession to the obvious Sebastian x Ciel scenes. (I love Sebastian x Ciel, and I am aware it's still kind of obvious later, but this season seems to be something else.)
And here's the other problem. Around halfway through the season, things started getting really confusing, and by the end things didn't make sense at all. After thinking things through repeatedly and re-watching a few episodes I understood what was going on, but it was still strange how things slowly began making no sense. Sebastian and Claude's quarrel messed things up because every aspect of it was constantly changing, Claude couldn't seem to decide what (or who) he wanted, and Alois was constantly having dramatically dangerous mood swings and also couldn't decide what or who he wanted.
To be honest, season two was still a lot better than season one, and I'm glad I watched it. But everything has its flaws.
